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ON MARGINAL INTEGRATION METHOD IN NONPARAMETRIC REGRESSION  

Lee, Young-Kyung (Department of Statistics, Seoul National University)
Publication Information
Journal of the Korean Statistical Society / v.33, no.4, 2004 , pp. 435-447 More about this Journal
Abstract
In additive nonparametric regression, Linton and Nielsen (1995) showed that the marginal integration when applied to the local linear smoother produces a rate-optimal estimator of each univariate component function for the case where the dimension of the predictor is two. In this paper we give new formulas for the bias and variance of the marginal integration regression estimators which are valid for boundary areas as well as fixed interior points, and show the local linear marginal integration estimator is in fact rate-optimal when the dimension of the predictor is less than or equal to four. We extend the results to the case of the local polynomial smoother, too.
Keywords
Marginal integration; local linear smoothing; backfitting; boundary properties;
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  • Reference
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